Question

Calculate the energy of wind per unit mass if the power available at the rotor of a wind turbine is 700 diameter of the rotor, D= 7500 cm, Air density, p = 1.23 kg/m and Power Coefficient, C, = 0.32

Answer 1

Given that,

Power = 700 kW

Diameter = 7500 cm

Air density = 1.23 kg/m³

Power coefficient C =0.32

We need to calculate the wind speed

Using formula of power

$P=\dfrac{1}{2}\times \rho\times A\times v^3\times C_{p}$

$v^3=\dfrac{2P}{\rho\times\pi\times r^2\times C_{p}}$

Put the value into the formula

$v^3=\dfrac{2\times700\times10^{3}}{1.23\times3.14\times(3750\times10^{-2})^2\times0.32}$

$v^3=805.52$

$v=(805.52)^{\frac{1}{3}}$

$v=9.30\ m/s$

We need to calculate the energy of wind per unit mass

Using formula of energy

$E=\dfrac{1}{2}mv^2$

$\dfrac{E}{m}=\dfrac{v^2}{2}$

Put the value into the formula

$\dfrac{E}{m}=\dfrac{9.30^2}{2}$

$\dfrac{E}{m}=43.25\ J/kg$

Hence, The energy of wind per unit mass is 43.25 J/kg.